A previous conceptual work, called the Cordus conjecture, has proposed a nonlocal hidden-variable (NLHV) design for the photon, and thereby proposed a solution to photon entanglement and wave-particle duality. This paper applies a systems design approach to extend the theory to matter, specifically to differentiate between the matter and antimatter species. This concept rests on two premises: that particules have span (physical separation between reactive ends); and that their externally emitted discrete forces have an energization sequence. Specific hidden-variable models are proposed for the electron, positron, and proton. This concept provides a better explanation of the difference between matter and antimatter in ways that make physical sense. It also provides foundational concepts from which new solutions to other problems, like annihilation and baryogenesis, can be envisaged. The Cordus theory goes beyond conventional NLHV solutions, such as the de Broglie–Bohm model, by offering a solution not only for the inner contents of a particle, the hiddenvariables, but also predicting how its discrete fields operate. This theory provides a physically natural explanation for spin, handedness, chirality, and related directional attributes of particles, which are otherwise only abstract concepts in quantum mechanics. The theory also explains parity violation, and why the photon does not have an antiparticle. This work makes a conceptual contribution of presenting a new concept of handedness and the matter–antimatter species differentiation. It demonstrates the potential of hidden-variable designs to provide solutions of high explanatory power.